Active fault detection and dual control in multiple model framework ⋆

The paper deals with active fault detection and dual control in the multiple model framework. A monitored and controlled system is described by a discrete-time linear stochastic model at each step of a finite time horizon. The model belongs to an a priori given set of models, and known transient probabilities describe switching between the models. The goal is to design an active detector and controller that processes all available information and generates decisions and inputs. The decisions inform whether a fault has occurred in the system, and the inputs should simultaneously control and excite the system. As the control is in conflict with the excitation, the dual control problem arises. It is shown that both active fault detection and dual control can be solved using Bellman’s principle of optimality, and a corresponding backward recursive equation is derived. The approximative solution of the backward recursive equation is discussed, and an algorithm based on an application of rolling horizon and nonlinear filtering techniques is presented. The presented approach is illustrated in a simple numerical example.